{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reproduction of `PhysRevLett.79.765`\n",
    "\n",
    "```bibtex\n",
    "@article{PhysRevLett.79.765,\n",
    "  title     = {{Nature of Driving Force for Protein Folding: A Result From Analyzing the Statistical Potential}},\n",
    "  author    = {Li, Hao and Tang, Chao and Wingreen, Ned S.},\n",
    "  journal   = {Phys. Rev. Lett.},\n",
    "  volume    = {79},\n",
    "  issue     = {4},\n",
    "  pages     = {765--768},\n",
    "  numpages  = {0},\n",
    "  year      = {1997},\n",
    "  month     = {Jul},\n",
    "  publisher = {American Physical Society},\n",
    "  doi       = {10.1103/PhysRevLett.79.765},\n",
    "  url       = {https://link.aps.org/doi/10.1103/PhysRevLett.79.765}\n",
    "}\n",
    "@article{10.1006/jmbi.1996.0114,\n",
    "  title    = {{Residue – Residue Potentials with a Favorable Contact Pair Term and an Unfavorable High Packing Density Term, for Simulation and Threading}},\n",
    "  journal  = {Journal of Molecular Biology},\n",
    "  volume   = {256},\n",
    "  number   = {3},\n",
    "  pages    = {623-644},\n",
    "  year     = {1996},\n",
    "  issn     = {0022-2836},\n",
    "  doi      = {https://doi.org/10.1006/jmbi.1996.0114},\n",
    "  url      = {https://www.sciencedirect.com/science/article/pii/S002228369690114X},\n",
    "  author   = {Sanzo Miyazawa and Robert L. Jernigan},\n",
    "  keywords = {hydrophobicity, contact energy, residue packing energy, sequence threading, sequence sampling weights}\n",
    "}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style('whitegrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MJ-Matrix: adopt the upper half of Table 3 in ref[10.1006/jmbi.1996.0114]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "mj_matrix_df = pd.read_csv('../data/mj_matrix.csv', index_col=0, skiprows=1)\n",
    "mj_matrix = mj_matrix_df.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "sns.heatmap(mj_matrix_df, square=True, cmap='RdBu_r')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{aligned}\n",
    "M_{ij}-\\langle M_{ij} \\rangle=\\sum_{\\alpha=1}^{N}\\lambda_{\\alpha}V_{\\alpha,i}V_{\\alpha,j}, \\quad \\text{Eq. }(1) \\\\\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "eig_vals, eig_vecs = np.linalg.eigh(mj_matrix-mj_matrix.mean())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Such a subtraction procedure is necessary to remove a trivial source of a large eigenvalue. Any matrix with a nonzero mean $m_0$ can have one dominant eigen-value proportional to $Nm_0$ if the dimension $N$ of the matrix is large. Removing this trivial regularity enables us to clearly identify other intrinsic regularities which could be obscured in the spectrum of the unsubtracted matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-22.50373575  -1.55596307  -1.07471276  -0.60086612  -0.47326171\n",
      "  -0.36414528  -0.2424168   -0.18057467  -0.09447336  -0.08476189\n",
      "  -0.0284157    0.02600764   0.07073561   0.15347803   0.30414512\n",
      "   0.32357128   0.39307364   0.7522797    2.38548112  18.73455497] \n",
      "min: 0.026, max: 2.385\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(eig_vals, \"\\nmin: {:.3f}, max: {:.3f}\".format(np.abs(eig_vals[1:-1]).min(), np.abs(eig_vals[1:-1]).max()))\n",
    "sns.lineplot(data=eig_vals)\n",
    "sns.scatterplot(data=eig_vals)\n",
    "plt.show()\n",
    "plt.bar(x=range(len(eig_vals)), height=np.abs(eig_vals))\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fO4I/HMGhmrGYTbicNu6YmRdfkARQ3ehjQ1kVeyob48fmTxnFypJCCkalnddnSbAnTwJeCHHBFk4by5PAK7ur8YQ0HDYr3792AjMmZgHQ4A3xyu5qPjh8Oj5FMz3PxaOlRcxsO6ejvZVNvLGvllOtAfIyHNw7dxLzLxstwX6RJOCFEEmZf9lorhqfiTek8eeKCqYU5uANRXhzXy2bD9QRisQqYyZkOVhVUkjJ5aMTBvXeyiZ++ckxLKZYRY6BzubPTpCXaafkit7LLkXvJOCFEBck0QrUiG7wzmd1/GbPcVqDscVL2U6VB+ZN5var87D0Uhnzxr5arGaFsRl2XHYLwXCUs94Q67ZXSsBfJAl4IcR5ad8qr9kfjj9A1Q2D7d+c5X//8TRn/bEad7tq4p7iSdwzZ2Knh7A98WkRikanEY4aNHrD6EaslW97RY5IngS8EKJPibbK+6ymmfVllRw9E2tFYlLg9pl5PDivgJw0a5/XNJsU0m0WikalUdXow2Y5t0VeQIsyMdvZ/z/ICCMBL4ToUVCL4vZr+MOR+EKlirNeNpRVsre6OX7etXl2fvTtq8nP6TuUTQqk21UyHSqq2cTyufmsfe8IUd3AoZoJaFG0qMGjpUUD9FONHBLwQohutGhsBaonpGG0JfuZ1iCv7K7moyNn4mE/Y3wGq0uLcAQb+gx3kwLpNpUMh9qpj3t7Rc4LZZXUNfuZmO3k0dKiPvvaiL5JwAsh4qK6QWsgTGuHB6ieoMbrn9bwzsET8V2W8nOcrCopZP6UUSiKQkVFQ4/XNClw9LSHdw6e5OgZD7kZ9m4BvnDaWAn0ASABL4SIP0BtCZzbKi8c0fk/B0/w+t4aPG2VMaPSrDw4v4DvzBiH2dR7bbqigMumUn7Szc8/PIqBgdNqpt4T7LUxmeg/EvBCjHD+UITmDg9QdcPg4/J6fr2zinpPCACn1czSOZO4u3giDtXc2+VQ4lMxFmwWM+u2V7aFu6XtWhb84Ui3xmSi/0nACzFCJXqAuq+6ifVllVScje3pYDEp3HHNeO7/Vj5Zzt4rY7oGe7u+GpOJgSMBL8QIk+gB6rEzHtaXVXKgpiV+3k1XjOGRBYVMyHL0ej1FgUynjfFZjk7B3i5RYzIpg7w0JOCFGCESPUA97Q7y611VfFxeHz9v1qRMVpcWMW1cRk+XAtq+sVtVXA4LoQYShjt0b0wmZZCXjgS8EIOo47Z3kwaoPDDRA1R3QOO1T4/zu0Mn48cKR6exqqSQ6wtzem3u1THY7W3z8YZh9Hi+lEEOHgl4IQZJ123vBqK6pOsK1JAW5Z22yhhfKHZsdLqVh28oZNGVub1WxijEHpBmOtV4sJ8vKYMcHBLwQgySrtve9Wd1SVCL0uLXCLQ9QI3qBh99dYZXdlVz1hurjEmzmVk+J5+7Zk/oNbDjwe5QsVsvLNjF4JKAF2KQDER1STgS2yrP2/YA1TAMPq1qYsOOKqoaYpUxqlnhzlkTuPf6fDK7fH5HCuCwWsiSYB+yJOCFGCT9WV2SqIXv16dbWV9WyaFad/y8W6eP5ZEbChmXae/xWgpgV81kOVUc59ENUqQu+V9PiEHSH9UlhmHgCWq0+M/tgXqiJcBLO6rYdvRs/Lzi/CxWlRYxNdfV6/XsFjOZTvW8N8AWqU3+VxRikFxsdYknpOH2aYSjsZ2Tmv1hXt1znC1fnIp/i58yJo3VpUXMKcjp9VpWs4nMNJV0q2yPN5xIwAsxiJKpLgmEIzT7NIJtlTEBLcrmA3W8ua8Wfzh2LDfDxiM3FHLL9LGYeglsi0khy6nisqsS7MOQBLwQQ0TX1gJR3eD3h0+zcXc1jb4wAC67hfuuz+fOWRM6teTtymxSyHTEgr2vpmFi6JKAFyLFJaqM2V3RyIs7qjjeFKu4Uc0Ki2dPZPncSbjsPVfGmE0KLruFDLva6z6pYniQgBciRUWisWD3BDXaptQ5ctLN+rJKvjzRCsQqXhZdlcvD8wsYm9FzZUzXXZTEyCABL0SKMQyD1oCGO3CuMqa2yc+LO6vYcezcxhpzC3NYVVLIlDHpPV6rvSd7112UxMggAS9ECvGGNFo6VMY0+cJs3FPN1i9Oxb/FX5HrYnVpIdfmZ/d4HYW21r3OWOveS9HzRqQeCXghUkDX1gL+cIS39tfx1v5aglos7PMy7axcUMiNV4zpsTImUb+YS9HzRqQmCXghBpEW1Wnxn3uAGonqbP3yNL/ZU02zXwMgw27h/nmT+f4143ucP+9t9elA9rwRqU0CXohB0LU3u2EYlB1r4KWdVdQ1BwCwWUzcXTyRpXMmkd7DytL2YM90qDh7OEd2VBq5JOCFuIQS9Wb/vK6F9WWVlJ/yALGKl29fNY4H5xcwxmXr8Vo2S+wbe19tBWRHpZErqYAPBoM8/vjjNDY2kpaWxtNPP01OTvel0E1NTSxbtowtW7Zgs/X8iyrESNC1N3t1o48NZVXsqWyMnzN/yihWlhRSMCqtx+tcaFsB2VFp5Eoq4Ddt2sTUqVN57LHH2Lp1K+vWreOnP/1pp3N27NjBM888Q0NDQw9XEWJk6PoA9awnxMbd1Xxw5HS8MmZ6notHS4uYOTGrx+vEHpJaSbdfWL8Y2VFp5FKM3vba6sGaNWtYuXIls2bNwuPxsGzZMrZu3drpnF27dnHllVeyePFifv/73/f5Df7QoUND5lt+MBjEbu95UclIIfchpqf7YChm/JpOa1AjGtXxazofHvPwcYWXcNv0zNg0C3ddmcHs8Y4eQ9umxlae2i0Ghq4P6M+SLPldiBms+zB9+vSEx/v8Bv/222+zcePGTsdGjRqFyxVrO5qWlobH4+n2vhtuuOGCBmiz2XocZKopLy8fMmMdSHIfYrreh4692e26gSuqs+Xzk7z6pxrcgVhlTLZT5YF5k7n96rweWwYMpX4x8rsQMxj3oby8vMfX+gz4JUuWsGTJkk7H1qxZg88X2x3G5/ORkdH77utCjAS6HuvN3r4CVTcMtn1zlpd2VnHKHQTArpq457pJ3HPdxE4PPTuSfjGivyQ1Bz979my2b9/OzJkzKSsro7i4uL/HJcSQoShKfNMNrW0F6mc1zawvq+ToGS8Qq4z53szxPDBvMjlp1oTXMZsU0m2xvU8l2EV/SCrgly9fzhNPPMHy5ctRVZVnnnkGgJdffpn8/HxuueWWfh2kEKnKG9JoDOhYPbGNrCvOetmwo4q9VU3xc0ouH82KBYXk5yQuS5RGYGKgJBXwDoeDZ599ttvxhx9+uNuxTz75JJmPECKlBcKxksegFsUf0qhvDfLy7mo+OnKG9qqFGeMzePTGIq4an5nwGooS6xeTKY3AxACRhU5CXIBQJLbphi8UK3n0BDU2H2nhk8oT8YVL+TlOVpUUMn/KqISVMQqQZrOQ4TjXL0aIgSABL8R50Dr0ZjeM2CYc7x46wWuf1uAJRgDISbPy0PwCvjNjXMKqFwVwWC1kOVTsVgl2MfAk4IXoRdeeMbph8Ifyen69q4ozrbF5d5tF4d65k7n7uok4evhGbm9rK9BTvxghBoL8tgmRgGEY8cqY9k039lU3saGsij+fjVXGmE0Kd8zMoyTP4NorJye8TntbAZet5230hBgoEvBCdOEJabg7bLpx7IyH9WWVHKhpiZ+zcOoYViwoZEK2g4qKim7XSLatgBD9SQJeiDb+tmZgwbZmYKfcAX69s5o/fF0fP+eaiZmsLi1iel7ixX2q+dzqUwl2Mdgk4MWIF9RilTH+tmZg7oDGa58e53eHTsYrYwpGOVldWsT1hTkJg9tiUshwqGTYVUwp3lZAjBwS8GLE0qI6br+Gp203pZAW5befnWDTvhp8odi3+NHpVh6+oZBFV+YmrIwxmxRGpTsYn+WQ1aci5UjAixGna2VMVDf46KszvLKrmrPeWGVMms3M8jn5LJ49AVuCyhiTAq621af++qiEu0hJEvBixGjfTanZHybStk3ep1VNbNhRRVVDrHmealb4wazx3Hf9ZDId3StfFAVcNpUMWX0qhgAJeDEieEMabr9GKBKrjPn6dCvryyo5VOuOn3Pr9LE8ckMh4zK79/OW1adiKJKAF8NaMByl2R8mqEUxgBMtAX69s4o/fnM2fk5xfharSouYmuvq9n5ZfSqGMgl4MSyFI7EHqN6QhgG0+MO8+qcatnx+Mr5wacqYNFaXFjGnoPt+wgpgV81kOmT1qRi65DdXDCuRDj1jdAMCWpTNB+p4c18t/nCsMmasy8YjCwq5dfpYTAlKHm0WE5lOlXRZfSqGOAl4MSzoukFr225K7ZUxvz98mo27q2n0hQFw2S3cd30+d86akPABqaw+FcONBLwY0tp7xrgDGlo0Vhmzu6KRF3dUcbzJD8SC+65rJ3Dv9fm47N2/lbfvfSqLlMRwIwEvhqyuPWOOnHSzvqySL0+0ArF59EVX5fLQ/AJyM7pXxnSsZZc6djEcScCLIScQjtDsO9czpqbJz0s7q9hxrCF+ztyCbFaVFDFlbHq390stuxgpJODFkNG1Z0yTL8zGPdVs/eIUbYUxTM1NZ3VpEbPzs7u9XwGcVguZTqllFyODBLxIeV17xvjDEd7aV8dbB2oJarHpmbxMOysWFLLwijHdKmMUwCYbbogRSH7bRcqKRHVagxqetp4xkajO1i9P8Zs9x2n2awBk2C08MG8yd1wzHrXLPHp7sGc6VdIk2MUIJL/1IuV0LXk0DIOyYw28tLOKuuYAEKtVv7t4IkvnTCI9QXhLLbsQEvAixcS2yQvH+7B/UdfC+rJKvjrlAWKVL9+eMY4H5xUwxmXr9n6pZRfiHAl4kRK6VsZUN/rYUFbFnsrG+DnzikaxqrSQglFp3d5vNilk2C1kOKwJ+7YLMRJJwItB1bUypsEb4pXd1Xxw+HS8MmZ6novVpUVcMzGr2/uVDrXsXefghRjpJODFoOhaGeMLRXhjXy2bD9TFW/pOzHawYkEhpZeP7jbd0t6+N9OpYrNIyaMQiUjAi0uqvRmYNxSrjNGiOls+P8mrf6rBHYhVxmQ5VB6YN5nvzczrtsK0vctjttMq7XuF6IMEvLgkovq5njFR3UA3DLZ9c5aXdlZxyh0EwK6auKd4EvfMmYjTmqgyJlbLLiWPQpwf+ZMiBlR7M7AWvxbvw/5ZTTPryyo5esYLxCpjbp+Zx4PzCshJs3a7hmpWyHJaSbdJZYwQF0ICXgwIwzDwhiOdmoFVnPWyoaySvdXN8fMWXDaalSWF5Oc4u13D0tbl0SVdHoVIigS8uGjbvq7nhbJKapv9TB3r4oF5k7k810WoreTxTGuQV3ZX89GRM7QVxjBjfAarS4uYMSGz2/Wk5FGI/pFUwAeDQR5//HEaGxtJS0vj6aefJien87Znr7zyClu3bgXgxhtvZM2aNRc/WpFytn1dz9r3jpBht3DZmDTcgTD/9N4R/vrGKUwf72LT3lp++1ldfOFSfo6TVSWFzJ8yqntlTFvJY5a07xWiXyQV8Js2bWLq1Kk89thjbN26lXXr1vHTn/40/nptbS3vvfceb7/9NoqicO+993Lrrbcybdq0fhu4SA2v7K5mfJYNi8lMozdMKKIT1XWe/eQYnlAETzACQE6alYfmF/CdGeO6fStXgHSbSobTIiWPQvSjpAL+wIEDrFy5EoDS0lLWrVvX6fVx48bx4osvYjbH/rBGIhFstu7LysXQZpjMuIMakahOSNNiD1RDERq84fgDVYdqZtncSdxdPBFHgha9DjVWGeNIUDUjhLg4ff6pevvtt9m4cWOnY6NGjcLlcgGQlpaGx+Pp9LqqquTk5GAYBj//+c+58sorKSws7PVzQqEQ5eXlFzr+QREMBofMWAeEyYwvrNPQ6sfv9+MORtENaA5G0aLnTru5KJ3vXeHCZYtwsqY6flwBbKpKltOCZjJo0fVL/iP0pxH/+4Dcg3apdh/6DPglS5awZMmSTsfWrFmDz+cDwOfzkZGR0e19oVCIf/iHfyAtLY1/+qd/6nMgNpuN6dOnn++4B1V5efmQGWt/iuoG7kAYTzCCTTdo9lWw6Op8XthRSThyLqTtqok1Cy/juzPzul1jOO5/OlJ/HzqSexAzGPeht/9DServxbNnz2b79u3MnDmTsrIyiouLO71uGAY//OEPuf7661m9enUyHyFSSHv73tbAuVr20+4gL+5v4tM6f/w8q1mhYFQaj9xQyNyizg/d27fJy3RKzxghLpWkAn758uU88cQTLF++HFVVeeaZZwB4+eWXyc/PR9d19u7dSzgcZseOHQD8+Mc/5tprr+2/kYsBZxgG3mCElsC59r3ugMZrnx7nd4dOxo8VjHKyurSI6wtzEvaMcVgtZMk2eUJcckkFvMPh4Nlnn+12/OGHH47/+5dffpn8qMSg84Y03H4t3vgrpEV55+AJXt9bgy8Um2jPsptZdeNlLLoyN2G9us1iIstpldYCQgwS+ZMnOgmEI7T4NYJaFIPYvPv//eoML++q5qw3BECa1czyuflcmx1m+tRx3a5hMSlkOWMrUKW1gBCDRwJeALG+7K0BDV8o1pfdMAw+rWpiw44qqhpiD9RVs8IPZo3nvusnk+lQqaio6HQNs0nBZbeQKStQhUgJEvAjXNe+7ADlp1pZX1bJ53Xu+Hm3TBvLIwsKyMt0dLuGPEAVIjVJwI9QHUseo22VMSdaAry0o4ptR8/GzyvOz2JVaRFTc13drmEyKaRZY5tuyANUIVKPBPwIk6jksdkf5tU9x9nyxal42F82Jp1VpYXMKchJeB27xUyuy05upv2SjV0IcWEk4EcIXTfwhjr3ZQ9oUTYfqOPNfbX4w7HKmLEuGysWFHLL9LGYEjwg7dib3X062u11IUTqkIAf5hLVskd1g98fPsXG3cdp9IUBcNkt3Hd9PnfOmoDV0n0evb2Fb6bDOmxWoAox3EnAD2OekNZpww3DMNhd0ciGHVXUNMVWoKpmhbuuncC91+fjsqvdrjEQD1A79o+flO3k0dIiFk4b2y/XFkKcIwE/DPlDbbXskXNTKF+dbOWFsgq+PNEKxFaYLroql4fmF5Cb0X0efaBWoLb3j1fNClkOlXpPkLXvHeFJkJAXop9JwA8D276u55Xd1bQGNUanW7lt+jiKC7IBqGny89LOKnYca4ifP7cgm1WlRUwZk57wegO5ufULZZWoZiW+qbbTasEfjvBCWaUEvBD9TAJ+iCv7pp7nPjmGxaSgRXXKT3n48kQrj8wv4IuTbrZ+cYq2Z6pMzU1ndWkRs/OzE17rUqxArW32k+XoPBXkUM3UNft7eIcQIlkS8ENYOKKzaW8t3lAkvkjJZjbhDoT41w++jgd7XqadR24o5KZpYxJWxlzKPVAnZTup9wTj3+AhVs0zMbv7pttCiIsjAT8EdVyk9FltMxl2CxjgDkRo9IWJtqV9ht3C/fMmc8fM8QkrYwZjBeqjpUWsfe8I/nAEh2omoEXRogaPlhZdks8XYiSRgB9CdN3AE9Rwd1ikNM5lp64lQGtQi5dBKsTq2Tc8eB3pCebRFSDNZiHDcelXoC6cNpYnic3F1zX7mShVNEIMGAn4ISBRLTvA53UtNPnD8Vp2iHV6TLNZ+NtbpyYMd7vFTHba4O6BunDaWAl0IS4BCfgUZhgG3nCkUy07QHWjjw1lVeypbIwfy7BbUM0Kk7LTWDZnUrcdlSwmhWynlXS7RVr4CjFCSMCnqNiGGxFCHWrZG7whXtldzQeHT8cfoE7Pc7G6tIhrJmYlvI5JAZddJcspLXyFGGkk4FOMPxTBHTi34QaANxThzX21bD5QF99haWK2g5ULCim5fHTCb+Tt8+yZThWbRTo9CjESScCniGA4SktAIxCOxINdi+ps+fwkv9lznNZgBIBsp8oD8yZz+9V5WHqofEmFeXYhxOCTBBhkXXdSAtANg23fnOWlnVWccgcBsJpNZDtVdAy2f9NAXoaj2zx7e6fHRD1lhBAjjwT8IAlHdNwBDW+HnZQADtY080JZJUfPeIHYHPqcghyqGnxYLSbsqolGX4hffnKMH3E5c4tyMJsUMh0qGXZVOj0KIeIk4C8xLRoLdk+wc7BXnvWyfkcVe6ua4scWXDaalSWF/Mf/PYbNYsLRVrPevkDod4dOcuuVubJVnhAiIQn4Abbt63pe3FGFOxhmUraTW6aP5doOvWDqW4O8vLuaj46ciU/RzBifwerSImZMyATgVGsgtlq1jc1iYmyGjUA4wmiX7VL+OEKIIUQCfgBt+7qeZz76BpfDgtVs4vAJNwdrW/jRzZczfbyLTXtr+e1ndfHFS/k5TlaVFDJ/yqhOlTF5GQ4afSFcNguZTit21cRZT0jm2oUQvZKAHyCGYbD5QC2KCZq8YXQD7KoZPRzh2U+O4QlF8LRVxuSkWXlo/mS+MyMvYa368jmT2PinarKcKtGoTk1TEC1q8L8WXXGpfywhxBAiAT8AvCGNFp/GZ7UtpFnNKCgYhoEnGKHBF473kXGoZpbNmcTd102Mz693ZTYpLJqRy/gsO78qq+SkOyD9W4QQ50UCvoOL3UrOF4rg9muEIrFFSmPT7TT6Qui6QYMvHF+kBHDnrPHcP28y2U5rwmspCqTbVLLaHqCWXDGWkisk0IUQ52/IB3x/7e95MVvJJVp9ClBy+Whe2FFJuEOw21UTaxZexndn5iW81kBtlSeEGHmGdMD35/6eyWwl1zHYP61s4o19tZxqDZDjtGJTzRyqbYmfazEpWEwKdouJj8vrGZ1u67ZQyWo2kZWmkm6Th6dCiIs3pAO+P/f3vJCt5HTMnHYH420F9lY28ctPjqEAIS1K+WlP/NyCUU5uvHwMH351GtWceKFSMlvl9dffXIQQw9eQXh1T2+zv9nAy2f09J2U7CWjRTse6biUXDEc57Q5y2hPE36FnzOt7a/CHI5xuDdISiFXGmBWYlO1gwwPX8XmdG9UcW6ikoOBQzVhMCls+P0mmQ2VCtpMMh/WCwn3te0eo9wQ7/c1l29f1F/xzCyGGryEd8OcTyufr0dIitKgRC24j9k8tavDDhVMIhqOccQc55Q7gD0fQ26pgorrB7w+f5vBJN+5ABN2ItRYYnWalYLQTLapjNimcag1gV8/dartqonC0E78WYVS67YLb+Hb8m4uixP6pmhVeKKu84J9bCDF8JTVFEwwGefzxx2lsbCQtLY2nn36anJzO88mvvfYa77zzDoqi8Dd/8zfcdNNN/TLgjvpzf8+uW8lNGZPOwzcUMDXXxSl3oNPDU8Mw+FNlIxt2VFHV4Isfz3KojEqL9V0PaFHGZTiAcwuVMuwWspxWrGYT9Z4gGY7EFTR9uZDpJCHEyJVUwG/atImpU6fy2GOPsXXrVtatW8dPf/rT+OtNTU28/vrrvPvuu4RCIW6//XYWLlzY7zsJ9ff+nu1byXXs8OgLRzqd8/XpVn65q4FvGk7Ej82amMkJdwC7xYzJFPtbREQ3WDZnEtC+UOk4mU4LWlTndGtsodLj/yO5jaYnZTup9wTjzx4g+b+5CCGGr6QC/sCBA6xcuRKA0tJS1q1b1+n1nJwcfve732GxWDhx4gQZGRkDtk1cf+7vGYpEafVH8IY7NwIDONES4KUdVWw7ejZ+rDg/i1WlRUzNdbG3rYrmdGuAcRmO+LZ5ZpPC/7h6HOOz7fxqWyWn+mGhUn/+zUUIMXwphtE1yjp7++232bhxY6djo0aNYu3atUyZMgVd11m4cCFlZWXd3vtf//VfPPfcc9x///2sWbOm14EcOnQIm+3SN85SFAUdEz5NxxPUiHbY+xTAE4ry/jcetld5ad/veoLLwpKrs7hqrL3H65pNJlwOlXSrCfRoj+cla1+dj81H3JzxRshNt3D3VZnMmZjW75/Tm2AwiN3e8z0YKeQ+yD1oN1j3Yfr06QmP9xnwiaxZs4bVq1czc+ZMPB4Py5cv5/333094bjgcZtWqVfz1X/813/rWt3q8Znl5eY+DvBi9lROGIzqtAQ1PqPs39oAWZfOBOt7cV4s/HAvosS4bKxYUUmD1cPlll/X4mQ7VTLbTit06vBcqDdT/ZkON3Ae5B+0G4z709plJTdHMnj2b7du3M3PmTMrKyiguLu70emVlJf/+7//Oc889h6qqWK1WTKZLX7CTaCHUk+9/hckEV47PxBvU4ptXt2uvjNm4u5pGXxgAl93Cfdfnc+esCVgtJioqvAk/T3ZUEkKkkqQCfvny5TzxxBMsX74cVVV55plnAHj55ZfJz8/nlltuYdq0aSxduhRFUSgpKWHu3Ln9OvDz0bGc0GxSyHOqRA2DF8oq+f9+MKPTuYZhsLsiVhlT0xSrRlHNCnddO4F7r8/vNbTNJgWX3UKmw3rBJY9CCDFQkgp4h8PBs88+2+34ww8/HP/3NWvW9DnvPtBqm/3kOFUy7BasFhPuoIYnoMU3sG535KSbF7ZXcvhkKxDrB7Poqlweml9AbkbP82kKsYZgmU4Vq2VILykQQgxDQ7pVQV+uHOfCG44QjERp8IbQDQhoerw+vabJz4s7qtj554b4e+YW5rCqpJApY9J7vK6iKNgtZrLTVBzWYX0LhRBD2LBMJ1038IY0vnt1Hr/46BtMioJdNRHUdCK6we1Xj+P///goW784FZ+DvyLXxerSwk7b6SViMSmMcdnJy7IPWOmnEEL0h2EV8IZh4A1FaPGH0aIGMydl8dhNl8fr08ek2xmbYeOZj48S1GLlkHmZdlYsKGThFWMw9RLYigIZdpUspxVffVTCXQiR8oZNwHtDWttmG53r2OcW5TB7chZbvzzFb/Yc58uTbgAy7BYemDeZO64Zj2ruef5cAdJsFjKdKjbL8C57FEIML0M+4P2hCC0ddlHqyDAMyo418NLOKuqaAwDYLCbuLp7I0jmTSLf1/uPbLGaynSrOPs4TQohUNGSTKxCO4A5E4j3Zu/qiroX1ZZV8dSrWm92kwLevGseD8wsY4+p9xWwy/dmFECLVDLmAD2pR3H6tUz/2jqobfby4o4rdFY3xY/OKRrGypJDC0b0v5VcUcNlVshwqll6mbYQQYigYMgEfbwQW0hIGe4M3xCu7q/ng8Ol4Zcz0PBerS4u4ZmJWr9eWeXYhxHCU8gHfW78YAF8owhv7atl8oC7+gHVitoMVCwopvXx0r1MsCmBXzWQ5pZ5dCDH8pGyqadG2YE/QL6b99S2fn+TVP9XgDmgAZDtVHpg3mduvzutzikU2uBZCDHcpF/BR3cAdCOMJRogmSHbdMNj2zVle2lnFKXcQiG2Bd891k7jnuomdNsFIRB6gCiFGipQJeMOAFn+Y1oBGJNFXduBgTTMvlFVy9Eysm6NJgduvzuPB+QXkpPW+/Z08QBVCjDQpE/C6YdDU1p63q8qzXtbvqGJvVVP8WMnlo1mxoJD8nN63qVMApzX2ANWuygNUIcTIkTIBn0h9a5CXd1fz0ZEz8cqZGeMzWF1axIwJmX2+32o2kZ1mJU0WKgkhRqCUTD5PUGPT3lreOXiCcFtlTH6Ok1UlhcyfMqrPuXOLSSHToZLhkHl2IcTIlVIBH47ovHvoBK99WoOnrWd7TpqVh+ZP5jsz8vrcTEPm2YUQ4pyUCXh3QOPHL+/lTGsIiO1rumzuJO4unoijj7lzWagkhBDdpUzA1zUHONMawmxSuGNmHvfPm0y2s/fKGEA23hBCiB6kVCounDqGFQsKmZDt6PNc1ayQlWbFJQuVhBAioZQJ+Km56cyZVdDneWaTQkbbBtcm2eBaCCF6lDIB39umG9D2ALVtg+u+zhVCCJFCAd8TWagkhBDJSemAt1tinR5lRyUhhLhwKTPXUd3o43+99Tn7KptQzQpjXDbysuwS7kIIkaSUCXizoqBFdX578ATVDT7p9iiEEBcpZQIeIMup0hIIs25b5WAPRQghhryUCfiIbtASiGA1m6hr9g/2cIQQYshLmYBvF9CiTMzuvQWwEEKIvqVMwBsY+MMRtKjBo6VFgz0cIYQY8lKmRCWqG4x12Xm0tIiF08YO9nCEEGLIS5mAnzYug003TR/sYQghxLCRMlM0Qggh+ldSAR8MBnnssce49957WbVqFU1NTQnP03WdlStXsmnTposapBBCiAuXVMBv2rSJqVOn8vrrr3PnnXeybt26hOf9x3/8B263+6IGKIQQIjlJBfyBAwcoKSkBoLS0lD179nQ754MPPkBRFEpLSy9uhEIIIZLS50PWt99+m40bN3Y6NmrUKFwuFwBpaWl4PJ5Orx89epT333+fZ599lueff/68BhIKhSgvLz/fcQ+qYDA4ZMY6kOQ+xMh9kHvQLtXuQ58Bv2TJEpYsWdLp2Jo1a/D5fAD4fD4yMjI6vf7uu+9y5swZHnzwQU6cOIGqqkyYMGHYfJu32+2DPYSUIPchRu6D3IN2g3EfQqFQj68lVSY5e/Zstm/fzsyZMykrK6O4uLjT63//938f//fnnnuO0aNH9xnus2bNSmYoQgghepDUHPzy5cs5duwYy5cv580332TNmjUAvPzyy/zhD3/o1wEKIYRIjmIYhjHYgxBCCNH/ZKGTEEIMUxLwQggxTEnACyHEMCUBL4QQw5QEfA90XWft2rUsXbqU+++/n+PHj3d6/ZNPPmHx4sUsXbqUt956a5BGOfD6ug8AgUCAZcuWUVFRMQgjvDT6ug/vv/8+S5YsYdmyZaxduxZd1wdppAOrr/vw4YcfsnjxYu6++27efvvtQRrlwDufPxcA//iP/8i//du/XeLRdWCIhD788EPjiSeeMAzDMA4ePGj81V/9Vfy1cDhs3HrrrUZLS4sRCoWMu+66y6ivrx+soQ6o3u6DYRjGF198YfzFX/yFMX/+fOPPf/7zYAzxkujtPgQCAeOWW24x/H6/YRiG8bd/+7fGxx9/PCjjHGi93YdIJGLcdtttRmtrqxGJRIxFixYZjY2NgzXUAdXXnwvDMIxNmzYZ99xzj/GLX/ziUg8vTr7B96Bjv51Zs2Zx+PDh+GsVFRXk5+eTmZmJ1WqluLiY/fv3D9ZQB1Rv9wEgHA7z/PPPU1Q0vHfh6u0+WK1W3njjDRwOBwCRSASbzTYo4xxovd0Hs9nMf//3f+NyuWhpaQFirUyGo77+XBw8eJDPP/+cpUuXDsbw4iTge+D1eklPT4//t9lsJhKJxF9r78UDsV9ir9d7ycd4KfR2HwCKi4vJy8sbjKFdUr3dB5PJxOjRowF49dVX8fv93HDDDYMyzoHW1++DxWLho48+4gc/+AHXXXcdFkvK7CnUr3q7D/X19fznf/4na9euHazhxUnA9yA9PT3ebwdic27tv6xdX/P5fJ0Cfzjp7T6MJH3dB13Xefrpp9m1axfPPfcciqIMxjAH3Pn8PixatIiysjI0TePdd9+9xCO8NHq7Dx988AHNzc2sXr2a9evX8/777/POO+8Myjgl4Hswe/ZsysrKADh06BBTp06NvzZlyhSOHz9OS0sL4XCY/fv3c+211w7WUAdUb/dhJOnrPqxdu5ZQKMS6deviUzXDUW/3wev18pd/+ZeEw2FMJhMOhwOTaXhGTG/34YEHHuCdd97h1VdfZfXq1Xzve9/jrrvuGpRxjryvYufptttuY9euXSxbtgzDMHjqqafYsmULfr+fpUuX8pOf/IQVK1ZgGAaLFy8mNzd3sIc8IPq6DyNFb/dhxowZbN68meuuu44HH3wQiP0hv+222wZ51P2vr9+HO+64g/vuuw+LxcIVV1zB97///cEe8oAYKn8upBeNEEIMU8Pz709CCCEk4IUQYriSgBdCiGFKAl4IIYYpCXghhBimJOCFEGKYkoAXQohh6v8BbZtfiQ+dQWEAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "LinregressResult(slope=0.9006478176988847, intercept=-0.29987045793258704, rvalue=0.9860156612041119, pvalue=1.8466913761714847e-15, stderr=0.035879570728644644, intercept_stderr=0.008022915915276112)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sns.regplot(x=eig_vecs[:, 0], y=eig_vecs[:, -1])\n",
    "plt.show()\n",
    "lr = scipy.stats.linregress(eig_vecs[:, 0], eig_vecs[:, -1])\n",
    "lr\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{aligned}\n",
    "\\tilde{M}_{ij}&\\approx\\langle M_{ij} \\rangle + \\lambda_{1}V_{1,i}V_{1,j} + \\lambda_{2}V_{2,i}V_{2,j} \\\\\n",
    "V_{2,i}&\\approx\\beta+\\gamma V_{1,i}, \\; (\\beta=-0.30,\\;\\gamma=0.90) \\\\\n",
    "\\\\\n",
    "\\Rightarrow \\tilde{M}_{ij}&\\approx C_{0} + C_{1}(q_{i}+q_{j}) + C_{2}q_{i}q_{j}, \\quad \\text{Eq. }(2) \\\\\n",
    "\\text{where}\\\\\n",
    "q_{i}&\\equiv V_{1,i}\\\\\n",
    "C_{0}&=\\langle M_{ij} \\rangle + \\beta^{2}\\lambda_{2}\\\\\n",
    "C_{1}&=\\beta\\gamma\\lambda_{2}\\\\\n",
    "C_{2}&=\\lambda_{1}+\\gamma^{2}\\lambda_{2}\\\\\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.4813458857210562, -5.059785022050667, -7.306892518528944)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C_0 = mj_matrix.mean()+((lr.intercept)**2)*eig_vals[-1]\n",
    "C_1 = lr.intercept * lr.slope * eig_vals[-1]\n",
    "C_2 = eig_vals[0] + (lr.slope**2)*eig_vals[-1]\n",
    "C_0, C_1, C_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "i_indices, j_indices = np.triu_indices(20)\n",
    "q = eig_vecs[:, 0]\n",
    "q_is = q[i_indices]\n",
    "q_js = q[j_indices]\n",
    "mj_matrix_triu_pred = C_0 + C_1*(q_is+q_js) + C_2*np.multiply(q_is, q_js)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x432 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "LinregressResult(slope=0.9750882154800643, intercept=-0.0788096884672278, rvalue=0.9886078126392621, pvalue=4.825757670139841e-173, stderr=0.01029357734637542, intercept_stderr=0.03622826390679035)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sns.jointplot(y=mj_matrix_triu_pred,x=mj_matrix[i_indices, j_indices], kind='reg')\n",
    "plt.show()\n",
    "scipy.stats.linregress(y=mj_matrix_triu_pred,x=mj_matrix[i_indices, j_indices])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Notice that one can redefine the $q$'s in Eq. (2) by a shift and rescaling while leaving the interaction form unchanged. Therefore any transformation $q \\rightarrow Aq + B$ with a corresponding change in the $C$'s yields an identical matrix.\n",
    "\n",
    "To better understand the physical meaning of Eq. (2), rewrite it as:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\tilde{M}_{ij}&=h_{i} + h_{j} - \\frac{C_{2}(q_{i}-q_{j})^{2}}{2}, \\quad \\text{Eq. }(3) \\\\\n",
    "\\text{where}\\\\\n",
    "h_{i}&=\\frac{C_{0}}{2}+C_{1}q_{i}+\\frac{C_{2}}{2} q_{i}^{2}\\\\\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "> Now each term in Eq. (3) above is invariant under the transformation discussed above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "h = C_0/2 + C_1 * q + C_2/2 * q**2\n",
    "\n",
    "mj_matrix_triu_pred_from_h = h[i_indices] + h[j_indices] - C_2/2 * (q_is - q_js)**2\n",
    "assert np.allclose(mj_matrix_triu_pred, mj_matrix_triu_pred_from_h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Comparison of the terms in Eq. (3) shows that the linear term $h_i + h_j$ is the dominant one in selecting the native structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x432 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "LinregressResult(slope=0.9980657756847827, intercept=-0.19685061953967686, rvalue=0.9793051326829264, pvalue=2.744235627334894e-146, stderr=0.014302012853078272, intercept_stderr=0.050335959851904546)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sns.jointplot(y=h[i_indices] + h[j_indices],\n",
    "              x=mj_matrix[i_indices, j_indices], kind='reg')\n",
    "plt.show()\n",
    "scipy.stats.linregress(y=h[i_indices] + h[j_indices],\n",
    "                       x=mj_matrix[i_indices, j_indices])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(h, bins=10)\n",
    "plt.show()\n",
    "sns.histplot(q, bins=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "sns.lineplot(x=q, y=h)\n",
    "ax = sns.scatterplot(x=q, y=h)\n",
    "for idx_idx, idx in enumerate(np.argsort(q)):\n",
    "    ax.text(q[idx]+0.005*(-1)**(idx_idx), h[idx]+0.12*(-1)**(idx_idx), mj_matrix_df.columns[idx])\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "2266c607543d224cb119288ea55888d6fda87cc9a4c78c02ed099d39082a76ce"
  },
  "kernelspec": {
   "display_name": "Python 3.7.9 ('base')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
